2 thoughts on “the motion of a particule in a central force field lies in a”
Answer:
If a particle moves in a central force field then the following properties hold: Page 2 1. The path of the particle must be a plane curve, i.e., it must lie in a plane. 2. The angular momentum of the particle is conserved, i.e., it is constant in time.
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In the Figure we see 4 positions P1,P2,P3,P4 of the moving particle with position vectors r1,r2,r3,r4. Under the influence of a central force the angular momentum vector L=r×mv is constant. The vectors r,v are the position and the velocity vector of the particle at an arbitrary time moment.
Answer:
If a particle moves in a central force field then the following properties hold: Page 2 1. The path of the particle must be a plane curve, i.e., it must lie in a plane. 2. The angular momentum of the particle is conserved, i.e., it is constant in time.
Hope it’s helpful to you
Please mark as brainliest and please give me thanks
In the Figure we see 4 positions P1,P2,P3,P4 of the moving particle with position vectors r1,r2,r3,r4. Under the influence of a central force the angular momentum vector L=r×mv is constant. The vectors r,v are the position and the velocity vector of the particle at an arbitrary time moment.
So
r1r2r3r4⊥L1=r1×mv1=r×mv=L⊥L2=r2×mv2=r×mv=L⊥L3=r3×mv3=r×mv=L⊥L4=r4×mv4=r×mv=L(01.1)(01.2)(01.3)(01.4)
that is the position vector rȷ(tȷ) at any time tȷ is normal to the constant vector L.
So all points Pȷ, all position vectors rȷ and consequently all velocity vectors vȷ lie on a plane perpendicular to L and we have plane motion.